Phase transitions and multifractal properties of random field Ising models:
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
2001
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Leipzig, Univ., Diss., 2001 |
| Physical Description: | 128 S. Ill., graph. Darst. |
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MARC
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| 100 | 1 | |a Nowotny, Thomas |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Phase transitions and multifractal properties of random field Ising models |c von Thomas Nowotny |
| 264 | 1 | |c 2001 | |
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| 500 | |a Leipzig, Univ., Diss., 2001 | ||
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Record in the Search Index
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|---|---|
| adam_text |
CONTENTS
1 INTRODUCTION 3
2 MULTIFRACTAL MEASURES 11
2.1 GENERALIZED FRACTAL DIMENSIONS.YY
YY
-. 11
2.2 RANDOM ITERATED FUNCTION SYSTEMS . 17
3 MULTIFRACTAL PROPERTIES OF THE EFFECTIVE FIELD OF THE ID RFIM 19
3.1 BASIC PROPERTIES AND NOTATIONS. 21
3.2 KNOWN TRANSITIONS IN THE DG-SPECTRUM. 22
3.3 POINTWISE DIMENSION OF ORBITS. 25
3.3.1 POINTWISE DIMENSION OF ORBITS OUTSIDE THE OVERLAP. 25
3.3.2 POINTWISE DIMENSION OF POINTS IN THE OVERLAP. 30
3.4 FURTHER TRANSITIONS IN THE D^-SPECTRUM. 32
3.4.1 TRANSITION AT . 32
3.4.2 TRANSITION AT . 34
3.4.3 TRANSITION DIAGRAM. 39
3.5 BOUNDS ON THE DG-SPECTRUM. 41
3.5.1 GENERAL RELATIONS BETWEEN
DQ
AND
DP
. 41
3.5.2 APPLICATION TO THE MEASURE OF THE EFFECTIVE FIELD. 44
4 CONVOLUTION OF MULTIFRACTALS AND THE LOCAL MAGNETIZATION OF THE
ID RFIM 48
4.1 CONVOLUTION OF MULTIFRACTALS.,YY. 49
4.2 CONVOLUTION OF CANTOR SETS WITH WEIGHTS. 58
4.3 THE D,-SPECTRUM OF THE LOCAL MAGNETIZATION. 62
4.3.1 THE APPROXIMATING MEASURE DENSITIES. 62
4.3.2 THE D
G-SPECTRUM. 66
5 RANDOM FIELD ISING MODEL ON THE BETHE LATTICE 71
5.1
UPPER BOUNDS FOR THE EXISTENCE OF A UNIQUE PARAMAGNETIC PHASE
. 73
5.2 APPROXIMATIONS OF THE TRANSITION LINE. 78
5.2.1 DIRECT CALCULATION OF THE MAGNETIZATION. 78
5.2.2 AVERAGE CONTRACTIVITY OF THE RANDOM ITERATED FUNCTION SYSTEM 80
1
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/963597159
2
CONTENTS
5.2.3 INDEPENDENCE OF THE EFFECTIVE FIELDS FROM BOUNDARY CONDITIONS 83
5.2.4 DISCUSSION. 85
5.3 MULTIFRACTAL PROPERTIES OF THE EFFECTIVE FIELD. 89
5.3.1 LEFT-SIDEDNESS OF THE INVARIANT MEASURE. 89
5.3.2 TRANSITION IN
D0 . 90
6 CONCLUSIONS 93
A NUMERICAL METHODS 99
A.L EFFECTIVE FIELD. 99
A. 1.1 BOX METHOD.100
A. 1.2 NATURAL PARTITION METHOD .102
A. 2 LOCAL MAGNETIZATION .103
A.2.1 CONVOLUTION.103
A.2.2 BOX METHOD.104
A.2.3 NATURAL PARTITION METHOD .105
B ADDITIONAL PROOFS 106
B. L MONOTONICITY OF
DQ.106
B.2 COVARIANCE OF DP WITH RESPECT TO BI-LIPSCHITZ MAPS.107
B.3 REFORMULATION OF THE PARTITION FUNCTION OF THE ID RFIM .107
B.4 REFORMULATION SCHEME FOR THE RFIM ON THE BETHE LATTICE.109
B.5 STRUCTURE OF THE RIFS .109
B.6 RELATION OF DP(X; FJ,^) AND DP(F~L(X);/J,^) ILL
B.7 PROOF OF LEMMA 3.2.ILL
B.8 PROOF OF LEMMA 3.4. 112
B.9 PROOF OF LEMMA 3.5.114
B.10 EQUIVALENCE OF GRID POSITIONS.115
B.LL CALCULATION OF DP(X*_;U) FOR THE RFIM ON THE BETHE LATTICE 115
BIBLIOGRAPHY 117
INDEX
127 |
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| illustrated | Illustrated |
| indexdate | 2024-10-09T18:06:14Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009648724 |
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| physical | 128 S. Ill., graph. Darst. |
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| spelling | Nowotny, Thomas Verfasser aut Phase transitions and multifractal properties of random field Ising models von Thomas Nowotny 2001 128 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Leipzig, Univ., Diss., 2001 Fraktal (DE-588)4123220-3 gnd rswk-swf Bethe-Gittermodell (DE-588)4208096-4 gnd rswk-swf Ferromagnetische Phasenumwandlung (DE-588)4341317-1 gnd rswk-swf Ising-Modell (DE-588)4127615-2 gnd rswk-swf Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Ising-Modell (DE-588)4127615-2 s Zufälliges Feld (DE-588)4191094-1 s Fraktal (DE-588)4123220-3 s DE-604 Bethe-Gittermodell (DE-588)4208096-4 s Ferromagnetische Phasenumwandlung (DE-588)4341317-1 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009648724&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nowotny, Thomas Phase transitions and multifractal properties of random field Ising models Fraktal (DE-588)4123220-3 gnd Bethe-Gittermodell (DE-588)4208096-4 gnd Ferromagnetische Phasenumwandlung (DE-588)4341317-1 gnd Ising-Modell (DE-588)4127615-2 gnd Zufälliges Feld (DE-588)4191094-1 gnd |
| subject_GND | (DE-588)4123220-3 (DE-588)4208096-4 (DE-588)4341317-1 (DE-588)4127615-2 (DE-588)4191094-1 (DE-588)4113937-9 |
| title | Phase transitions and multifractal properties of random field Ising models |
| title_auth | Phase transitions and multifractal properties of random field Ising models |
| title_exact_search | Phase transitions and multifractal properties of random field Ising models |
| title_full | Phase transitions and multifractal properties of random field Ising models von Thomas Nowotny |
| title_fullStr | Phase transitions and multifractal properties of random field Ising models von Thomas Nowotny |
| title_full_unstemmed | Phase transitions and multifractal properties of random field Ising models von Thomas Nowotny |
| title_short | Phase transitions and multifractal properties of random field Ising models |
| title_sort | phase transitions and multifractal properties of random field ising models |
| topic | Fraktal (DE-588)4123220-3 gnd Bethe-Gittermodell (DE-588)4208096-4 gnd Ferromagnetische Phasenumwandlung (DE-588)4341317-1 gnd Ising-Modell (DE-588)4127615-2 gnd Zufälliges Feld (DE-588)4191094-1 gnd |
| topic_facet | Fraktal Bethe-Gittermodell Ferromagnetische Phasenumwandlung Ising-Modell Zufälliges Feld Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009648724&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nowotnythomas phasetransitionsandmultifractalpropertiesofrandomfieldisingmodels |